In wireless communication, if both the transmitting end and the receiving end use a plurality of antennae, a higher rate can be obtained by means of space multiplexing. With respect to the general space multiplexing method, an enhanced technology is that the receiving end feeds back the channel state information to the transmitting end, and the transmitting end uses some transmission pre-coding techniques according to the obtained channel state information, thereby greatly improving the transmission performance. A simple utilization method is to perform pre-coding directly using the channel feature vector information, which is mainly used in single-user MIMO. There are also some other methods that are more preferable but more complicated, which are mainly used in multi-user MIMO.
The concept of layer is defined at the transmitting end, each layer can transmit different data symbols on the same time frequency resource, and the number of layers is equal to the Rank of channel matrix. If the complete channel state information can be known accurately at the transmitting end, linear or non-linear pre-coding can be performed on the data on the layer using the obtained CSI, so that the Signal-to-Noise ratio of the data received by the user when reaching the receiving end is the maximum, and the inter-layer interference and inter-user interference are the minimum.
If the channel state information can be accurately obtained, the optimal pre-coding can be achieved. However, channel state information (CSI) generally can only be obtained directly and accurately at the receiving end, and generally the CSI can only be obtained by the transmitting end through the receiving end, which feeds back the CSI to the transmitting end. An important issue problem is how to efficiently quantify the fed back CSI information. In the current mainstream standards, the feedback capacity provided for the CSI by the system is relatively limited, and since the feedback quantity of feeding back the whole channel state information is very large, the mainstream feedback methods are all based on the quantization modes of the codebook.
The basic principle of channel state information quantization feedback based on the codebook is as follows: if it is assumed that the limited feedback channel capacity is B bps/Hz, the number of available codewords is N=2B. The feature vector space of the channel matrix constitutes, after being quantified, the codebook space ={F1, F2L FN}. The transmitting end and the receiving end jointly store or generate in real time the codebook space (the same at the transmitting and receiving ends). For each time of channel implementation H, the receiving end selects from , according to a certain rule, a codeword {circumflex over (F)} mostly matched with the channel, and feeds the sequence number i of the codeword back to the transmitting end. The transmitting end finds out the pre-coded codeword {circumflex over (F)} according to the sequence number and obtains the channel state information, which is mainly the feature vector information of the channel.
Generally,  may be further divided into codebooks corresponding to a plurality of Ranks, each Rank corresponds to a plurality of codewords for quantifying a pre-coded matrix constituted by feature vectors of the channel matrix under the Rank. Since the number of Ranks of the channel and the number of non-zero feature vectors are the same, there are generally N columns of codewords when the number of Ranks is N. Therefore, the codebook  can be divided into a plurality of sub-codebooks according to the Rank, as shown in Table 1.
In a case where the CSI can be obtained completely and accurately, the performance of pre-coding according to the CSI is the best, and due to the limit of feedback overhead, codebook-based channel state information quantization feedback is usually adopted.
TABLE 1 Number of layers υ (Rank)12. . .N 1 2. . . NSet ofSet of codewordSet of codewordcodewordmatrices ofmatrices of column Nvectors ofcolumn 2column 1
Wherein, when Rank>1, the codewords that need to be stored are all in a form of matrix, for example the codebook in the Long Term Evolution (LTE) protocol precisely adopts this codebook quantization feedback method, as shown in Table 2. Hereinafter, the vector can also be regarded as a matrix with one of the dimensions being 1 for the purpose of consistence.
The LTE downlink 4Tx codebook is as shown in Table 2, and the meaning of pre-coded codebook in LTE is actually the same with that of the channel state information quantization codebook.
TABLE 2CodebookTotal number of layers υIndexun12340u0 = [1 −1 −1 −1]TW0{1}W0{14}/{square root over (2)}W0{124}/{square root over (3)}W0{1234}/21u1 = [1 −j 1 j]TW1{1}W1{12}/{square root over (2)}W1{123}/{square root over (3)}W1{1234}/22u2 = [1 1 −1 1]TW2{1}W2{12}/{square root over (2)}W2{123}/{square root over (3)}W2{3214}/23u3 = [1 j 1 −j]TW3{1}W3{12}/{square root over (2)}W3{123}/{square root over (3)}W3{3214}/24u4 = [1 (−1 − j)/{square root over (2)} −j (1 − j)/{square root over (2)}]TW4{1}W4{14}/{square root over (2)}W4{124}/{square root over (3)}W4{1234}/25u5 = [1 (1 − j)/{square root over (2)} j (−1 − j)/{square root over (2)}]TW5{1}W5{14}/{square root over (2)}W5{124}/{square root over (3)}W5{1234}/26u6 = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{square root over (2)}]TW6{1}W6{13}/{square root over (2)}W6{134}/{square root over (3)}W6{1324}/27u7 = [1 (−1 + j)/{square root over (2)} j (1 + j)/{square root over (2)}]TW7{1}W7{13}/{square root over (2)}W7{134}/{square root over (3)}W7{1324}/28u8 = [1 −1 1 1]TW8{1}W8{12}/{square root over (2)}W8{124}/{square root over (3)}W8{1234}/29u9 = [1 −j −1 −j]TW9{1}W9{14}/{square root over (2)}W9{134}/{square root over (3)}W9{1234}/210u10 = [1 1 1 −1]TW10{1}W10{13}/{square root over (2)}W10{123}/{square root over (3)}W10{1324}/211u11 = [1 j −1 j]TW11{1}W11{13}/{square root over (2)}W11{134}/{square root over (3)}W11{1324}/212u12 = [1 −1 −1 1]TW12{1}W12{12}/{square root over (2)}W12{123}/{square root over (3)}W12{1234}/213u13 = [1 −1 1 −1]TW13{1}W13{13}/{square root over (2)}W13{123}/{square root over (3)}W13{1324}/214u14 = [1 1 −1 −1]TW14{1}W14{13}/{square root over (2)}W14{123}/{square root over (3)}W14{3214}/215u15 = [1 1 1 1]TW15{1}W15{12}/{square root over (2)}W15{123}/{square root over (3)}W15{1234}/2
Wherein, Wn=I−2ununH/unHun, I is a unit matrix, Wk(j) represents the jth column of vectors of the matrix Wk. Wk(j1,j2, . . . jn) represents a matrix constituted by the j1th, j2th, . . . , jnth columns of the matrix Wk.
With the development of communication technology, the advanced Long Term Evolution (LTE-Advance) has higher requirements on the spectrum efficiency, so the number of antennae also increases to 8. For this, it needs to design a 8Tx codebook to perform quantization feedback of channel state information. The main application form of the 8 antennae is dual-polarized antennae, so it needs to design a codebook suitable for dual-polarized channels, and quantization feedback of channel state information is performed using this codebook.
When the CSI can be obtained completely and accurately, the performance of pre-coding is the best. Due to the limit of feedback overhead (the channel capacity used for feedback), it can only use the codebook based CSI feedback and pre-coding of the transmitted data symbols. In the practical MIMO system, the design of the codebook is very important, and one of the important objects of codebook design is to ensure that the quantization error is the minimum, and the codebook is simple to implement, the overhead is reasonable, and the storage amount is small.
Besides, in consideration of some specific applications, the codebook design should also have the following features.
1. Constant model feature: it is considered during the codebook design that the row vector of each pre-coded codeword in the codebook has the constant model feature so that the power distributed to each antenna after pre-coding is equal, thereby avoiding increase of the index of Peak to Average Power Ratio (PAPR), and the power amplification between various Power Amplifiers (PA) is balanced. Therefore, the basic requirement for constant model feature is that each row of the pre-coded matrix has the same model value, and when Rank=1, the constant model feature requires that the model values of various elements are equal.
2. Orthogonal feature: after Singular Value Decomposition (SVD) is performed on the channel matrix, each obtained right feature vector is bound to be orthogonal. The codebook is designed to be matched with the right feature vector direction of the channel matrix, so the designed codeword should also conform to this feature. In a pre-coded codeword where Rank>1, each column of vectors should be orthogonal. The orthogonal feature is an important principle, and no matter how the codebook is designed, the feature must be met so as to ensure the quantization accuracy of the codebook.
3. 8PSK feature: in consideration of the complexity of achieving pre-coding processing at the transmitting and receiving ends, it needs to define that the value of each element has to be selected from the points corresponding to 8 Phase Shift Keying (PSK), which is called as 8PSK feature. The codebook is defined to have the 8PSK feature, i.e., before normalization processing is performed on the codebook, the value of each element has to be selected from a letter set
  {      1    ,          -      1        ,    j    ,          -      j        ,                  1        +        j                    2              ,                            -          1                +        j                    2              ,                  1        -        j                    2              ,                            -          1                -        j                    2              }of 8PSK.
The LTE 4Tx codebook can better meet these rules.
The existing codebook used for channel state information quantization feedback mainly considers the channel applied by single-polarized antenna of the transmitting end, and the channels are distinguished in relevance in this antenna configuration, and the codewords that are suitable for high-relevant channel and independent channel features are used.
One of the directions of the current codebook design is that the completely independently irrelevant channel is considered for some codewords, i.e., each element in the channel (the channel between each pair of transmitting and receiving antennae is represented as a channel element in the channel matrix) is independently irrelevant (i.i,d), in which case the method for designing irrelevant channel codeword in the codebook where Rank is υ is as follows:
finding a plurality of matrices of υ columns (degrading to a vector when υ is 1) such that these multiple matrices (i.e., sub-spaces) are evenly distributed in the total space, where the main means is to use the method of Grassmannian line compression or sub-space compression to find the multiple codeword matrices evenly distributed in the total space.
The other direction is to consider the single-polarized array antenna scene with smaller antenna space. The channels are highly relevant, and at this moment the channels are not independently irrelevant, the feature vector represents a fixed model, for example when there are 8 antennae, the feature vector of the single-polarized antenna strongly-relevant channel is [1 ejθ ej2θ ej3θ . . . ej7θ], wherein θ indicates different phase values. Such a model has the same model with the column vector of the Discrete Fourier Transform (DFT) matrix, therefore, the columns of the DFT matrix are selected as the codewords of the relevant channel.
The existing feedback apparatus and codebook designing idea are applied to various mainstream standards, for example, 3GPP and LTE adopt such apparatus and method.
However, the existing codebook design for channel state information quantification feedback mainly concerns the relevant and irrelevant statuses of single-polarized antenna channel. When there are 8 antennae, dual-polarized antennae have much wider application prospect in the practical application due to the antenna space, especially when the number of antennae is greater than or equal to 4, so dual-polarized antennae have become the mainstream application gradually. Nevertheless, some features represented by the dual-polarized antennae are usually very complicated, for example a dual-polarized relevant channel only shows high relevance in the same polarization direction, but does not have high relevance between polarized directions, while a dual-polarized irrelevant channel shows independent nature in the same polarization direction but the relationship shown between polarized directions is not independent. Therefore, in the prior art, the codebook design method of relevant channels and irrelevant channels in the case of single-polarized antenna cannot match the channel features well in a channel of dual-polarized antennae, and its performance in the dual-polarized channel is very bad.
Currently, the existing codebook design technologies all consider single-polarized antennae, and there is no good method for feeding back channel state information of dual-polarized channels.